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(* Title: HOL/Tools/Sledgehammer/sledgehammer_isar.ML
Author: Jasmin Blanchette, TU Muenchen
Author: Steffen Juilf Smolka, TU Muenchen
Isar proof reconstruction from ATP proofs.
*)
signature SLEDGEHAMMER_ISAR =
sig
type atp_step_name = ATP_Proof.atp_step_name
type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step
type 'a atp_proof = 'a ATP_Proof.atp_proof
type stature = ATP_Problem_Generate.stature
type one_line_params = Sledgehammer_Proof_Methods.one_line_params
val trace : bool Config.T
type isar_params =
bool * (string option * string option) * Time.time * real option * bool * bool
* (term, string) atp_step list * thm
val proof_text : Proof.context -> bool -> bool option -> bool -> (unit -> isar_params) -> int ->
one_line_params -> string
end;
structure Sledgehammer_Isar : SLEDGEHAMMER_ISAR =
struct
open ATP_Util
open ATP_Problem
open ATP_Problem_Generate
open ATP_Proof
open ATP_Proof_Reconstruct
open Sledgehammer_Util
open Sledgehammer_Proof_Methods
open Sledgehammer_Isar_Proof
open Sledgehammer_Isar_Preplay
open Sledgehammer_Isar_Compress
open Sledgehammer_Isar_Minimize
structure String_Redirect = ATP_Proof_Redirect(
type key = atp_step_name
val ord = fn ((s, _ : string list), (s', _)) => fast_string_ord (s, s')
val string_of = fst)
open String_Redirect
val trace = Attrib.setup_config_bool \<^binding>\<open>sledgehammer_isar_trace\<close> (K false)
val e_definition_rule = "definition"
val e_skolemize_rule = "skolemize"
val leo2_extcnf_forall_neg_rule = "extcnf_forall_neg"
val satallax_skolemize_rule = "tab_ex"
val vampire_skolemisation_rule = "skolemisation"
val veriT_la_generic_rule = "la_generic"
val veriT_simp_arith_rule = "simp_arith"
val veriT_skolemize_rules = Verit_Proof.skolemization_steps
val z3_skolemize_rule = Z3_Proof.string_of_rule Z3_Proof.Skolemize
val z3_th_lemma_rule_prefix = Z3_Proof.string_of_rule (Z3_Proof.Th_Lemma "")
val zipperposition_cnf_rule = "cnf"
val skolemize_rules =
[e_definition_rule, e_skolemize_rule, leo2_extcnf_forall_neg_rule, satallax_skolemize_rule,
spass_skolemize_rule, vampire_skolemisation_rule, z3_skolemize_rule,
zipperposition_cnf_rule] @ veriT_skolemize_rules
fun is_ext_rule rule = (rule = leo2_extcnf_equal_neg_rule)
val is_maybe_ext_rule = is_ext_rule orf String.isPrefix satallax_tab_rule_prefix
val is_skolemize_rule = member (op =) skolemize_rules
fun is_arith_rule rule =
String.isPrefix z3_th_lemma_rule_prefix rule orelse rule = veriT_simp_arith_rule orelse
rule = veriT_la_generic_rule
fun raw_label_of_num num = (num, 0)
fun label_of_clause [(num, _)] = raw_label_of_num num
| label_of_clause c = (space_implode "___" (map (fst o raw_label_of_num o fst) c), 0)
fun add_global_fact ss = apsnd (union (op =) ss)
fun add_fact_of_dependency [(_, ss as _ :: _)] = add_global_fact ss
| add_fact_of_dependency names = apfst (insert (op =) (label_of_clause names))
fun add_line_pass1 (line as (name, role, t, rule, [])) lines =
(* No dependencies: lemma (for Z3), fact, conjecture, or (for Vampire) internal facts or
definitions. *)
if role = Conjecture orelse role = Negated_Conjecture then
line :: lines
else if t aconv \<^prop>\<open>True\<close> then
map (replace_dependencies_in_line (name, [])) lines
else if role = Lemma orelse role = Hypothesis orelse is_arith_rule rule then
line :: lines
else if role = Axiom then
lines (* axioms (facts) need no proof lines *)
else
map (replace_dependencies_in_line (name, [])) lines
| add_line_pass1 line lines = line :: lines
fun add_lines_pass2 res [] = rev res
| add_lines_pass2 res ((line as (name, role, t, rule, deps)) :: lines) =
let
fun normalize role =
role = Conjecture ? (HOLogic.dest_Trueprop #> s_not #> HOLogic.mk_Trueprop)
val norm_t = normalize role t
val is_duplicate =
exists (fn (prev_name, prev_role, prev_t, _, _) =>
(prev_role = Hypothesis andalso prev_t aconv t) orelse
(member (op =) deps prev_name andalso
Term.aconv_untyped (normalize prev_role prev_t, norm_t)))
res
fun looks_boring () = t aconv \<^prop>\<open>False\<close> orelse length deps < 2
fun is_skolemizing_line (_, _, _, rule', deps') =
is_skolemize_rule rule' andalso member (op =) deps' name
fun is_before_skolemize_rule () = exists is_skolemizing_line lines
in
if is_duplicate orelse
(role = Plain andalso not (is_skolemize_rule rule) andalso
not (is_ext_rule rule) andalso not (is_arith_rule rule) andalso
not (null lines) andalso looks_boring () andalso not (is_before_skolemize_rule ())) then
add_lines_pass2 res (map (replace_dependencies_in_line (name, deps)) lines)
else
add_lines_pass2 (line :: res) lines
end
type isar_params =
bool * (string option * string option) * Time.time * real option * bool * bool
* (term, string) atp_step list * thm
val basic_systematic_methods = [Metis_Method (NONE, NONE), Meson_Method, Blast_Method, SATx_Method]
val basic_simp_based_methods = [Auto_Method, Simp_Method, Fastforce_Method, Force_Method]
val basic_arith_methods = [Linarith_Method, Presburger_Method, Algebra_Method]
val arith_methods = basic_arith_methods @ basic_simp_based_methods @ basic_systematic_methods
val systematic_methods =
basic_systematic_methods @ basic_arith_methods @ basic_simp_based_methods @
[Metis_Method (SOME full_typesN, NONE), Metis_Method (SOME no_typesN, NONE)]
val rewrite_methods = basic_simp_based_methods @ basic_systematic_methods @ basic_arith_methods
val skolem_methods = Moura_Method :: systematic_methods
fun isar_proof_text ctxt debug num_chained isar_proofs smt_proofs isar_params
(one_line_params as ((used_facts, (_, one_line_play)), banner, subgoal, subgoal_count)) =
let
val _ = if debug then writeln "Constructing Isar proof..." else ()
fun generate_proof_text () =
let
val (verbose, alt_metis_args, preplay_timeout, compress, try0, minimize, atp_proof0, goal) =
isar_params ()
in
if null atp_proof0 then
one_line_proof_text ctxt 0 one_line_params
else
let
val systematic_methods' = insert (op =) (Metis_Method alt_metis_args) systematic_methods
fun massage_methods (meths as meth :: _) =
if not try0 then [meth]
else if smt_proofs then SMT_Method SMT_Z3 :: meths
else meths
val (params, _, concl_t) = strip_subgoal goal subgoal ctxt
val fixes = map (fn (s, T) => (Binding.name s, SOME T, NoSyn)) params
val ctxt = ctxt |> Variable.set_body false |> Proof_Context.add_fixes fixes |> snd
val do_preplay = preplay_timeout <> Time.zeroTime
val compress =
(case compress of
NONE => if isar_proofs = NONE andalso do_preplay then 1000.0 else 10.0
| SOME n => n)
fun is_fixed ctxt = Variable.is_declared ctxt orf Name.is_skolem
fun skolems_of ctxt t = Term.add_frees t [] |> filter_out (is_fixed ctxt o fst) |> rev
fun get_role keep_role ((num, _), role, t, rule, _) =
if keep_role role then SOME ((raw_label_of_num num, t), rule) else NONE
val trace = Config.get ctxt trace
val string_of_atp_steps =
let val to_string = ATP_Proof.string_of_atp_step (Syntax.string_of_term ctxt) I in
enclose "[\n" "\n]" o cat_lines o map (enclose " " "," o to_string)
end
val atp_proof = atp_proof0
|> trace ? tap (tracing o prefix "atp_proof0 = " o string_of_atp_steps)
|> (fn x => fold_rev add_line_pass1 x [])
|> add_lines_pass2 []
|> trace ? tap (tracing o prefix "atp_proof = " o string_of_atp_steps)
val conjs =
map_filter (fn (name, role, _, _, _) =>
if member (op =) [Conjecture, Negated_Conjecture] role then SOME name else NONE)
atp_proof
val assms = map_filter (Option.map fst o get_role (curry (op =) Hypothesis)) atp_proof
fun add_lemma ((label, goal), rule) ctxt =
let
val (skos, proof_methods) =
(if is_skolemize_rule rule then (skolems_of ctxt goal, skolem_methods)
else if is_arith_rule rule then ([], arith_methods)
else ([], rewrite_methods))
||> massage_methods
val prove = Prove {
qualifiers = [],
obtains = skos,
label = label,
goal = goal,
subproofs = [],
facts = ([], []),
proof_methods = proof_methods,
comment = ""}
in
(prove, ctxt |> not (null skos) ? (Variable.add_fixes (map fst skos) #> snd))
end
val (lems, _) =
fold_map add_lemma (map_filter (get_role (curry (op =) Lemma)) atp_proof) ctxt
val bot = #1 (List.last atp_proof)
val refute_graph =
atp_proof
|> map (fn (name, _, _, _, from) => (from, name))
|> make_refute_graph bot
|> fold (Atom_Graph.default_node o rpair ()) conjs
val axioms = axioms_of_refute_graph refute_graph conjs
val tainted = tainted_atoms_of_refute_graph refute_graph conjs
val is_clause_tainted = exists (member (op =) tainted)
val steps =
Symtab.empty
|> fold (fn (name as (s, _), role, t, rule, _) =>
Symtab.update_new (s, (rule, t
|> (if is_clause_tainted [name] then
HOLogic.dest_Trueprop
#> role <> Conjecture ? s_not
#> fold exists_of (map Var (Term.add_vars t []))
#> HOLogic.mk_Trueprop
else
I))))
atp_proof
fun is_referenced_in_step _ (Let _) = false
| is_referenced_in_step l (Prove {subproofs, facts = (ls, _), ...}) =
member (op =) ls l orelse exists (is_referenced_in_proof l) subproofs
and is_referenced_in_proof l (Proof {steps, ...}) =
exists (is_referenced_in_step l) steps
fun insert_lemma_in_step lem
(step as Prove {qualifiers, obtains, label, goal, subproofs, facts = (ls, gs),
proof_methods, comment}) =
let val l' = the (label_of_isar_step lem) in
if member (op =) ls l' then
[lem, step]
else
let val refs = map (is_referenced_in_proof l') subproofs in
if length (filter I refs) = 1 then
[Prove {
qualifiers = qualifiers,
obtains = obtains,
label = label,
goal = goal,
subproofs =
map2 (fn false => I | true => insert_lemma_in_proof lem) refs subproofs,
facts = (ls, gs),
proof_methods = proof_methods,
comment = comment}]
else
[lem, step]
end
end
and insert_lemma_in_steps lem [] = [lem]
| insert_lemma_in_steps lem (step :: steps) =
if is_referenced_in_step (the (label_of_isar_step lem)) step then
insert_lemma_in_step lem step @ steps
else
step :: insert_lemma_in_steps lem steps
and insert_lemma_in_proof lem (proof as Proof {steps, ...}) =
isar_proof_with_steps proof (insert_lemma_in_steps lem steps)
val rule_of_clause_id = fst o the o Symtab.lookup steps o fst
val finish_off = close_form #> rename_bound_vars
fun prop_of_clause [(num, _)] = Symtab.lookup steps num |> the |> snd |> finish_off
| prop_of_clause names =
let
val lits =
map (HOLogic.dest_Trueprop o snd) (map_filter (Symtab.lookup steps o fst) names)
in
(case List.partition (can HOLogic.dest_not) lits of
(negs as _ :: _, pos as _ :: _) =>
s_imp (Library.foldr1 s_conj (map HOLogic.dest_not negs),
Library.foldr1 s_disj pos)
| _ => fold (curry s_disj) lits \<^term>\<open>False\<close>)
end
|> HOLogic.mk_Trueprop |> finish_off
fun maybe_show outer c = if outer andalso eq_set (op =) (c, conjs) then [Show] else []
fun isar_steps outer predecessor accum [] =
accum
|> (if tainted = [] then
(* e.g., trivial, empty proof by Z3 *)
cons (Prove {
qualifiers = if outer then [Show] else [],
obtains = [],
label = no_label,
goal = concl_t,
subproofs = [],
facts = sort_facts (the_list predecessor, []),
proof_methods = massage_methods systematic_methods',
comment = ""})
else
I)
|> rev
| isar_steps outer _ accum (Have (id, (gamma, c)) :: infs) =
let
val l = label_of_clause c
val t = prop_of_clause c
val rule = rule_of_clause_id id
val skolem = is_skolemize_rule rule
val deps = ([], [])
|> fold add_fact_of_dependency gamma
|> is_maybe_ext_rule rule ? add_global_fact [short_thm_name ctxt ext]
|> sort_facts
val meths =
(if skolem then skolem_methods
else if is_arith_rule rule then arith_methods
else systematic_methods')
|> massage_methods
fun prove subproofs facts = Prove {
qualifiers = maybe_show outer c,
obtains = [],
label = l,
goal = t,
subproofs = subproofs,
facts = facts,
proof_methods = meths,
comment = ""}
fun steps_of_rest step = isar_steps outer (SOME l) (step :: accum) infs
in
if is_clause_tainted c then
(case gamma of
[g] =>
if skolem andalso is_clause_tainted g then
let
val skos = skolems_of ctxt (prop_of_clause g)
val subproof = Proof {fixes = skos, assumptions = [], steps = rev accum}
in
isar_steps outer (SOME l) [prove [subproof] ([], [])] infs
end
else
steps_of_rest (prove [] deps)
| _ => steps_of_rest (prove [] deps))
else
steps_of_rest
(if skolem then
(case skolems_of ctxt t of
[] => prove [] deps
| skos => Prove {
qualifiers = [],
obtains = skos,
label = l,
goal = t,
subproofs = [],
facts = deps,
proof_methods = meths,
comment = ""})
else
prove [] deps)
end
| isar_steps outer predecessor accum (Cases cases :: infs) =
let
fun isar_case (c, subinfs) =
isar_proof false [] [(label_of_clause c, prop_of_clause c)] [] subinfs
val c = succedent_of_cases cases
val l = label_of_clause c
val t = prop_of_clause c
val step =
Prove {
qualifiers = maybe_show outer c,
obtains = [],
label = l,
goal = t,
subproofs = map isar_case (filter_out (null o snd) cases),
facts = sort_facts (the_list predecessor, []),
proof_methods = massage_methods systematic_methods',
comment = ""}
in
isar_steps outer (SOME l) (step :: accum) infs
end
and isar_proof outer fixes assumptions lems infs =
let val steps = fold_rev insert_lemma_in_steps lems (isar_steps outer NONE [] infs) in
Proof {fixes = fixes, assumptions = assumptions, steps = steps}
end
val canonical_isar_proof =
refute_graph
|> trace ? tap (tracing o prefix "Refute graph:\n" o string_of_refute_graph)
|> redirect_graph axioms tainted bot
|> trace ? tap (tracing o prefix "Direct proof:\n" o string_of_direct_proof)
|> isar_proof true params assms lems
|> postprocess_isar_proof_remove_show_stuttering
|> postprocess_isar_proof_remove_unreferenced_steps I
|> relabel_isar_proof_canonically
val ctxt = ctxt |> enrich_context_with_local_facts canonical_isar_proof
val preplay_data = Unsynchronized.ref Canonical_Label_Tab.empty
val _ = fold_isar_steps (fn meth =>
K (set_preplay_outcomes_of_isar_step ctxt preplay_timeout preplay_data meth []))
(steps_of_isar_proof canonical_isar_proof) ()
fun str_of_preplay_outcome outcome =
if Lazy.is_finished outcome then string_of_play_outcome (Lazy.force outcome) else "?"
fun str_of_meth l meth =
string_of_proof_method [] meth ^ " " ^
str_of_preplay_outcome
(preplay_outcome_of_isar_step_for_method (!preplay_data) l meth)
fun comment_of l = map (str_of_meth l) #> commas
fun trace_isar_proof label proof =
if trace then
tracing (timestamp () ^ "\n" ^ label ^ ":\n\n" ^
string_of_isar_proof ctxt subgoal subgoal_count
(comment_isar_proof comment_of proof) ^ "\n")
else
()
fun comment_of l (meth :: _) =
(case (verbose,
Lazy.force (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth)) of
(false, Played _) => ""
| (_, outcome) => string_of_play_outcome outcome)
val (play_outcome, isar_proof) =
canonical_isar_proof
|> tap (trace_isar_proof "Original")
|> compress_isar_proof ctxt compress preplay_timeout preplay_data
|> tap (trace_isar_proof "Compressed")
|> postprocess_isar_proof_remove_unreferenced_steps
(keep_fastest_method_of_isar_step (!preplay_data)
#> minimize ? minimize_isar_step_dependencies ctxt preplay_data)
|> tap (trace_isar_proof "Minimized")
|> `(preplay_outcome_of_isar_proof (!preplay_data))
||> (comment_isar_proof comment_of
#> chain_isar_proof
#> kill_useless_labels_in_isar_proof
#> relabel_isar_proof_nicely
#> rationalize_obtains_in_isar_proofs ctxt)
in
(case (num_chained, add_isar_steps (steps_of_isar_proof isar_proof) 0) of
(0, 1) =>
one_line_proof_text ctxt 0
(if is_less (play_outcome_ord (play_outcome, one_line_play)) then
(case isar_proof of
Proof {steps = [Prove {facts = (_, gfs), proof_methods = meth :: _, ...}],
...} =>
let
val used_facts' =
map_filter (fn s =>
if exists (fn (s', (sc, _)) => s' = s andalso sc = Chained)
used_facts then
NONE
else
SOME (s, (Global, General))) gfs
in
((used_facts', (meth, play_outcome)), banner, subgoal, subgoal_count)
end)
else
one_line_params) ^
(if isar_proofs = SOME true then "\n(No Isar proof available.)" else "")
| (_, num_steps) =>
let
val msg =
(if verbose then [string_of_int num_steps ^ " step" ^ plural_s num_steps]
else []) @
(if do_preplay then [string_of_play_outcome play_outcome] else [])
in
one_line_proof_text ctxt 0 one_line_params ^
"\n\nIsar proof" ^ (commas msg |> not (null msg) ? enclose " (" ")") ^ ":\n" ^
Active.sendback_markup_command
(string_of_isar_proof ctxt subgoal subgoal_count isar_proof)
end)
end
end
in
if debug then
generate_proof_text ()
else
(case try generate_proof_text () of
SOME s => s
| NONE =>
one_line_proof_text ctxt 0 one_line_params ^
(if isar_proofs = SOME true then "\nWarning: Isar proof construction failed" else ""))
end
fun isar_proof_would_be_a_good_idea (_, play) =
(case play of
Played _ => false
| Play_Timed_Out time => time > Time.zeroTime
| Play_Failed => true)
fun proof_text ctxt debug isar_proofs smt_proofs isar_params num_chained
(one_line_params as ((_, preplay), _, _, _)) =
(if isar_proofs = SOME true orelse
(isar_proofs = NONE andalso isar_proof_would_be_a_good_idea preplay) then
isar_proof_text ctxt debug num_chained isar_proofs smt_proofs isar_params
else
one_line_proof_text ctxt num_chained) one_line_params
end;
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